Araştırma Makalesi
BibTex RIS Kaynak Göster

A new connection in a Riemannian manifold

Yıl 2008, Cilt: 1 Sayı: 1, 15 - 24, 30.04.2008

Öz

In a Riemannian manifold, the existence of a new connection is
proved. In particular cases, this connection reduces to several symmetric,
semi-symmetric and quarter-symmetric connections; even some of them are
not introduced so far. We also found formula for curvature tensor of this new
connection.

Kaynakça

  • [1] Agashe, N. S. and Chafle, M. R., A semi-symmetric non-metric connection in a Riemannian manifold, Indian J. Pure Appl. Math., 23(1992), 399-409.
  • [2] Andonie, O. C. and Smaranda, D., Certaines connexions semi-symmetriques, Tensor (N.S.),31(1977), 8-12.
  • [3] Eisenhart, L. P., Continuous groups of transformations, Dover Publications, Inc., New York, 1961.
  • [4] Friedmann, A. and Schouten, J. A., Über die geometrie der halbsymmetrischen Äubertragung, Math. Zeitschr. 21(1924), 211-223.
  • [5] Folland, G. B., Weyl manifolds, J. Dif. Geometry, 4(1970), 145-153.
  • [6] Golab, S., On semi-symmetric and quarter-symmetric linear connections, Tensor (N.S.), 29(1975), 249-254.
  • [7] Hayden, H. A., Subspaces of a space with torsion, Proc. London Math. Soc., 34(1932), 27-50.
  • [8] Liang, Y., On semi-symmetric recurrent-metric connection, Tensor (N.S.), 55(1994), 107-112.
  • [9] Mishra, R. S. and Pandey, S. N., On quarter-symmetric metric F-connections, Tensor (N.S.), 34(1980), 1-7. [10] Ojha, R. H. and Prasad, S., Semi-symmetric metric s-connection in a Sasakian manifold, Indian J. Pure Appl. Math., 16(1985), no. 4, 341-344.
  • [11] Pak, E., On the pseudo-Riemannian spaces, J. Korean Math. Soc., 6(1969), 23-31.
  • [12] Rastogi, S. C., On quarter-symmetric metric connection, C. R. Acad. Bulg. Sci., 31(1978), no. 8, 811-814.
  • [13] Rastogi, S. C., On quarter-symmetric metric connections, Tensor (N.S.), 44(1987), 133-141.
  • [14] Schmidt, B. G., Conditions on a connection to be a metric connection, Commun. Math. Phys., 29(1973), 55-59.
  • [15] Schouten, J. A., Ricci calculus, Springer, 1954.
  • [16] Sengupta, J. , De, U. C. and Binh, T. Q., On a type of semi-symmetric non-metric connection on a Riemannian manifold, Indian J. Pure Appl. Math., 31(2000), no. 12, 1659-1670.
  • [17] Smaranda, D., On projective transformations of symmetric connections with a recurrent projective tensor field, Proc. Nat.Coll. on Geometry and Topology (Busteni, 1981), 323-329, Univ. Bucaresti, Bucharest, 1983.
  • [18] Tamassy, L. and Binh, T. Q., On the non-existence of certain connections with torsion and of constant curvature, Publ. Math. Debrecen, 36(1989), 283-288.
  • [19] Yano, K., Integral formulas in Riemannian geometry, Marcel Dekker Inc., 1970.
  • [20] Yano, K., On semi-symmetric metric connections, Rev. Roumaine Math. Pures Appl. 15(1970), 1579-1586.
  • [21] Yano, K. and Imai, T., On semi-symmetric metric Á-connections in a Sasakian manifold, Kodai Math. Sem. Rep. 28(1977), 150-158.
  • [22] Yano, K. and Imai, T., Quarter-symmetric metric connections and their curvature tensors, Tensor (N.S.), 38(1982), 13-18.
Yıl 2008, Cilt: 1 Sayı: 1, 15 - 24, 30.04.2008

Öz

Kaynakça

  • [1] Agashe, N. S. and Chafle, M. R., A semi-symmetric non-metric connection in a Riemannian manifold, Indian J. Pure Appl. Math., 23(1992), 399-409.
  • [2] Andonie, O. C. and Smaranda, D., Certaines connexions semi-symmetriques, Tensor (N.S.),31(1977), 8-12.
  • [3] Eisenhart, L. P., Continuous groups of transformations, Dover Publications, Inc., New York, 1961.
  • [4] Friedmann, A. and Schouten, J. A., Über die geometrie der halbsymmetrischen Äubertragung, Math. Zeitschr. 21(1924), 211-223.
  • [5] Folland, G. B., Weyl manifolds, J. Dif. Geometry, 4(1970), 145-153.
  • [6] Golab, S., On semi-symmetric and quarter-symmetric linear connections, Tensor (N.S.), 29(1975), 249-254.
  • [7] Hayden, H. A., Subspaces of a space with torsion, Proc. London Math. Soc., 34(1932), 27-50.
  • [8] Liang, Y., On semi-symmetric recurrent-metric connection, Tensor (N.S.), 55(1994), 107-112.
  • [9] Mishra, R. S. and Pandey, S. N., On quarter-symmetric metric F-connections, Tensor (N.S.), 34(1980), 1-7. [10] Ojha, R. H. and Prasad, S., Semi-symmetric metric s-connection in a Sasakian manifold, Indian J. Pure Appl. Math., 16(1985), no. 4, 341-344.
  • [11] Pak, E., On the pseudo-Riemannian spaces, J. Korean Math. Soc., 6(1969), 23-31.
  • [12] Rastogi, S. C., On quarter-symmetric metric connection, C. R. Acad. Bulg. Sci., 31(1978), no. 8, 811-814.
  • [13] Rastogi, S. C., On quarter-symmetric metric connections, Tensor (N.S.), 44(1987), 133-141.
  • [14] Schmidt, B. G., Conditions on a connection to be a metric connection, Commun. Math. Phys., 29(1973), 55-59.
  • [15] Schouten, J. A., Ricci calculus, Springer, 1954.
  • [16] Sengupta, J. , De, U. C. and Binh, T. Q., On a type of semi-symmetric non-metric connection on a Riemannian manifold, Indian J. Pure Appl. Math., 31(2000), no. 12, 1659-1670.
  • [17] Smaranda, D., On projective transformations of symmetric connections with a recurrent projective tensor field, Proc. Nat.Coll. on Geometry and Topology (Busteni, 1981), 323-329, Univ. Bucaresti, Bucharest, 1983.
  • [18] Tamassy, L. and Binh, T. Q., On the non-existence of certain connections with torsion and of constant curvature, Publ. Math. Debrecen, 36(1989), 283-288.
  • [19] Yano, K., Integral formulas in Riemannian geometry, Marcel Dekker Inc., 1970.
  • [20] Yano, K., On semi-symmetric metric connections, Rev. Roumaine Math. Pures Appl. 15(1970), 1579-1586.
  • [21] Yano, K. and Imai, T., On semi-symmetric metric Á-connections in a Sasakian manifold, Kodai Math. Sem. Rep. 28(1977), 150-158.
  • [22] Yano, K. and Imai, T., Quarter-symmetric metric connections and their curvature tensors, Tensor (N.S.), 38(1982), 13-18.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Mukut Mani Tripathi

Yayımlanma Tarihi 30 Nisan 2008
Yayımlandığı Sayı Yıl 2008 Cilt: 1 Sayı: 1

Kaynak Göster

APA Mani Tripathi, M. (2008). A new connection in a Riemannian manifold. International Electronic Journal of Geometry, 1(1), 15-24.
AMA Mani Tripathi M. A new connection in a Riemannian manifold. Int. Electron. J. Geom. Nisan 2008;1(1):15-24.
Chicago Mani Tripathi, Mukut. “A New Connection in a Riemannian Manifold”. International Electronic Journal of Geometry 1, sy. 1 (Nisan 2008): 15-24.
EndNote Mani Tripathi M (01 Nisan 2008) A new connection in a Riemannian manifold. International Electronic Journal of Geometry 1 1 15–24.
IEEE M. Mani Tripathi, “A new connection in a Riemannian manifold”, Int. Electron. J. Geom., c. 1, sy. 1, ss. 15–24, 2008.
ISNAD Mani Tripathi, Mukut. “A New Connection in a Riemannian Manifold”. International Electronic Journal of Geometry 1/1 (Nisan 2008), 15-24.
JAMA Mani Tripathi M. A new connection in a Riemannian manifold. Int. Electron. J. Geom. 2008;1:15–24.
MLA Mani Tripathi, Mukut. “A New Connection in a Riemannian Manifold”. International Electronic Journal of Geometry, c. 1, sy. 1, 2008, ss. 15-24.
Vancouver Mani Tripathi M. A new connection in a Riemannian manifold. Int. Electron. J. Geom. 2008;1(1):15-24.